Distributed Quantiles Estimation of Sensor Network Measurements

Abstract

A quantile is a value below which random draws from a distribution falls with a given probability. In a centralized setting where the cumulative distribution function (CDF) is unknown, empirical CDF can be used to estimate quantiles after data aggregation. In a distributed sensor network, it is challenging to estimate quantiles, as each sensor observes local measurement data with limited storage and transmission power, which makes it difficult to obtain the global ECDF. This paper proposes consensus-based quantile estimation for such networks, even when communication links are corrupted by independent random noise. The state-values are recursively updated with two steps: a local update based on measurement data and current state and averaging updated states with local nodes. The estimated state sequence is shown to be asymptotically unbiased and converges toward the sample quantile in the mean-square sense. Applications on the distributed estimation of trimmed mean; computation of median, maximum, or minimum values; and identification of outliers through simulation are also provided.